Response of an under-damped system

ABSTRACT

An embodiment of a circuit for driving an under-damped system comprises first and second signal generators. The first generator is operable to generate a first drive signal. And the second generator is operable to receive the first drive signal and a second drive signal, and to generate from the first and second drive signals a system drive signal having a first amplitude for a first duration and having a second amplitude after the first duration, the system drive signal operable to cause the under-damped system to operate in a substantially damped manner. Either or both of the first and second generators may be programmable such that one may adjust the response of any under-damped system by generating an appropriate drive signal instead of by physically modifying the system itself. In another embodiment, an under-damped system is caused to oscillate at a damped frequency having a first phase, and is also caused to oscillate at substantially the damped frequency having a second phase such that the oscillation at the first phase substantially cancels the oscillation at the second phase. Such embodiments may allow one to realize a faster settling time without slowing down the response time of an under-damped system.

PRIORITY CLAIM

The instant application claims priority to Chinese Patent ApplicationNo. 200911000096.7, filed Dec. 31, 2009, which application isincorporated herein by reference in its entirety.

SUMMARY

An embodiment of a circuit for driving an under-damped system includesfirst and second signal generators. The first generator is operable togenerate a first drive signal. And the second generator is operable toreceive the first drive signal and a second drive signal, and togenerate from the first and second drive signals a system drive signalhaving a first amplitude for a first duration and having a secondamplitude after the first duration, the system drive signal operable tocause the under-damped system to operate in a substantially dampedmanner. Either or both of the first and second generators may beprogrammable such that one may adjust the response of any under-dampedsystem by generating an appropriate drive signal instead of byphysically modifying the system itself.

In another embodiment, an under-damped system is caused to oscillate ata damped frequency having a first phase, and is also caused to oscillateat substantially the same damped frequency having a second phase, suchthat the oscillation at the first phase substantially cancels theoscillation at the second phase.

Such embodiments may allow one to realize a faster settling time withoutslowing down the response time of an under-damped system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of an embodiment of a spring-loaded electromagneticlens assembly.

FIG. 2 is a plot of the step response of an embodiment of the assemblyof FIG. 1.

FIG. 3A is a plot of an embodiment of a drive waveform that may improvethe response of an embodiment of the lens assembly of FIG. 1 by reducingthe overshoot/undershoot and settling time of the assembly.

FIG. 3B is a plot of the response of an embodiment of the lens assemblyof FIG. 1 when driven with the drive waveform of FIG. 3A.

FIG. 4A is a plot of another embodiment of a drive waveform that mayimprove the response of an embodiment of the lens assembly of FIG. 1 byreducing the overshoot and settling time of the lens assembly.

FIG. 4B is a plot of the components of the response of an embodiment ofthe lens assembly of FIG. 1 when driven by the drive waveform of FIG.4A.

FIG. 4C is a plot of the overall response (i.e., sum of the responsecomponents) of an embodiment of the lens assembly of FIG. 1 when drivenby the drive waveform of FIG. 4A.

FIG. 5 is a diagram of an embodiment of a drive circuit for driving anembodiment of the lens assembly of FIG. 1 with an embodiment of thewaveform of FIG. 4A.

FIG. 5A is a diagram of an embodiment of a programmable signal generatorof FIG. 5.

FIG. 6 is a diagram of another embodiment of a drive circuit for drivingan embodiment of the assembly of FIG. 1 with an embodiment of thewaveform of FIG. 4A.

FIG. 7 is a diagram of a system that may incorporate an embodiment ofthe lens assembly of FIG. 1 and an embodiment of a drive circuit ofFIGS. 5 and 6.

DETAILED DESCRIPTION

FIG. 1 is a diagram of an embodiment of a spring-loaded electromagneticlens assembly 10, which includes a focusable lens 12. The lens assembly10 may be part of a system such as a camera or video recorder (not shownin FIG. 1). An example of such a lens assembly is shown in U.S. Pat. No.7,612,957, which is incorporated by reference.

In addition to the lens 12, the lens assembly 10 includes a spring 14for forcing the lens toward a reference location 16, and includes a coil18 and at least one permanent magnet 20 (two magnets shown in FIG. 1),which cooperate to force the lens away from the reference location.Because one may model the lens assembly 10 as a second-order spring-masssystem, a damper 22 is included in FIG. 1 to represent a level ofdamping inherent in the lens assembly—the damper is not an actualcomponent of the lens assembly, but represents the combination of all ofthe sources of damping, such as the stiffness of the spring 14 and anyfriction that the lens 12 may encounter as it moves. The coil 18 mayinclude an electrical resistance, an indication of which is omitted fromFIG. 1. Furthermore, the combination of the spring 14, coil 18, and atleast one magnet 20 is sometimes referred to as a spring-loadedvoice-coil motor (vcm).

In operation, the system (e.g., a camera) in which the lens assembly 10is installed determines (e.g., with an auto-focus circuit not shown inFIG. 1) a position of the lens 12 for proper focusing, and generates andsends a corresponding drive voltage V_(coil) to the coil 18. Because thelens 12 is to “step” from its current position to a focus position, thesystem “steps” the drive voltage V_(coil) such that when V_(coil) isapplied across the coil 18, the resulting current I_(coil) through thecoil is sufficient to move the lens to, and thereafter maintain the lensat, the focus position.

For example, assume that the lens 12 is currently in a position x₁relative to the reference location 16, and that the focus position x₂(the position of the lens 12 shown in FIG. 1) is farther away from thereference location 16 than is x₁.

Therefore, to move the lens 12 from x₁ to x₂, the system substantiallysteps the voltage V_(coil) across the coil 18 from a starting coilvoltage V_(coil)=V₁ to an ending coil voltage V_(coil)=V₂ that is higherthan V₁.

Because the coil 18 acts as an inductor, although the current I_(coil)through the coil increases, it does not step from one value to another,at least not as quickly as the voltage V_(coil) from V₁ to V₂. But overa period of time that depends, e.g., on the inductance of the coil 18,the drive voltage V₂ does cause the coil current I_(coil) to increasefrom a starting current I_(coil)=I₁ to an ending currentI_(coil)=V₂/R_(coil)=I₂ that is greater than I₁, where R_(coil) is theresistance of the coil 18 (R_(coil) is omitted from FIG. 1).

As the coil current I_(coil) increases, the magnitude of the magneticfield generated by the coil 18 increases, and this increasing coilmagnetic field interacts with the magnetic field generated by themagnets 20 so as to increase the net magnetic force F_(magnetic) in adirection away from the reference location 16.

As F_(magnetic) increases and becomes larger than the spring forceF_(spring), it causes the lens 12 to move away from the referencelocation 16.

Therefore, F_(magnetic) continues to increase, and the lens 12 continuesto move, until I_(coil) reaches I₂, at which time F_(magnetic) reachesits steady-state value and the lens 12 approximately attains theposition x₂, which is the position of the lens 12 shown in FIG. 1.

The lens 12 remains approximately in the position x₂ as long as V_(coil)and I_(coil) remain at V₂ and I₂ respectively.

Still referring to FIG. 1, alternate embodiments of the lens assembly 10are contemplated. For example instead of pulling the lens 12 toward thereference location 16, the spring 14 may push the lens away from thereference location; and instead of forcing the lens away from thereference location, the combination of the coil 18 and magnets 20 mayforce the lens toward the reference location

Referring to FIG. 2, a potential problem with the lens assembly 10 isdescribed.

FIG. 2 is a plot of the position of the lens 12 versus time for anunder-damped embodiment of the lens assembly 10 of FIG. 1, where thevoltage V_(coil) across the coil 18 is theoretically steppedinstantaneously from V_(coil)=V₁ to V_(coil)=V₂. Although an actualinstantaneous stepping of V_(coil) from V₁ to V₂ may be impractical orimpossible, a theoretical stepping of V_(coil) from V₁ to V₂ allows oneto examine the step response of the lens assembly 10, and to thus gainan insight into the operation of the lens assembly when V_(coil) isincreased from V₁ to V₂ in a relatively short time.

Referring to FIGS. 1 and 2, if the lens assembly 10 is under-damped(i.e., the damping level is relatively low) and the coil voltageV_(coil) is quickly increased from V₁ to V₂ to move the lens 12 from x₁to x₂, then the lens 12 overshoots x₂, and oscillates around x₂ in anexponentially decaying manner for a period of time. A step response of asystem where the system initially overshoots, and then oscillates about,a final steady-state value (here position x₂) may be called anunder-damped step response. For example, as shown in FIG. 2, anembodiment of the lens 12 may initially overshoot x₂ by approximately80% of the difference between x₁ and x₂, and the time required for theamplitude of this oscillation to settle to 10% of the difference betweenx₁ and x₂ may be approximately 150 milliseconds (ms). A similar analysisalso applies of V₁ is greater than V₂ and x₁ is greater than x₂, inwhich case the lens 12 may undershoot its desired new focus position x₂.

Unfortunately, a relatively poor under-damped response such as shown inFIG. 2 may render the lens assembly 10 of FIG. 1 unsuitable for someapplications. For example, an embodiment of the lens assembly 10 withthe under-damped response of FIG. 2 may be unsuitable for use in apocket-digital-camera application because the assembly takes too long tomove the lens 12 between steady-state focus positions.

One technique for reducing the overshoot/undershoot and settling time ofa second-order system such as the lens assembly 10 is to increase thedamping level of the assembly. But increasing the damping level mayincrease the power required to move the lens 12 from one position toanother, and this increased power may be unsuitable for someapplications, such as an application where the lens assembly 10 isbattery powered.

Another technique for reducing the overshoot/undershoot and settlingtime of a second-order system such as the lens assembly 10 is describedin conjunction with FIGS. 3A and 3B.

FIG. 3A is a plot of an embodiment of the coil voltage V_(coil) withwhich a system may drive the coil 18 of FIG. 1.

FIG. 3B is a plot of the response of an embodiment of the lens assembly10 of FIG. 1 when the coil 18 is driven with V_(coil) of FIG. 3A.

Referring to FIG. 3A, instead of changing the coil 18 drive voltageV_(coil) as quickly as possible, the system in which the lens assembly10 is installed may lengthen the time over which it changes V_(coil).For example, the system may increase V_(coil) from V₁ to V₂ in a seriesof steps having substantially the same voltage magnitude andsubstantially the same duration.

But referring to FIG. 3B, even increasing the time over which the systemchanges the drive voltage V_(coil) may fail to render an embodiment ofthe lens assembly 10 suitable for some applications. Although increasingthe time over which V_(coil) is changed may reduce the amplitude of theovershoot/undershoot, it may also increase the settling time to anunsuitable level. That is, increasing the time over which V_(coil) isincreased/decreased to achieve a suitable level of overshoot/undershootin the lens assembly 10 may undesirably increase the settling time ofthe lens assembly to an unsuitable level.

Referring to FIGS. 4A-4C, another technique for reducing theovershoot/undershoot amplitude and the settling time of an under-dampedembodiment of the lens assembly 10 (or of any other under-dampedsecond-order system) is described.

FIG. 4A is a plot of an embodiment of a multi-component voltage V_(coil)with which a system may drive the coil 18 of FIG. 1.

FIG. 4B is a plot of the respective responses of an embodiment of thelens assembly 10 of FIG. 1 to the V_(coil) components of FIG. 4A.

FIG. 4C is a plot of the overall response of an embodiment of the lensassembly 10 of FIG. 1 to V_(coil) of FIG. 4A.

Referring to FIGS. 4A-4C, in general, an embodiment of the technique isto drive a second-order system (e.g., the lens assembly 10 of FIG. 1)with a multi-component drive signal such that the decaying oscillationscaused by each of the drive-signal components substantially cancel oneanother. That is, once the system reaches a desired new position, itsubstantially remains there. Consequently, the effective settling timeis approximately equal to the time required for the system to firstreach the new position. Furthermore, the system may reach the newposition more quickly than if the system's physical level of dampingwere increased to reduce overshoot/undershoot

For example, referring to FIGS. 1 and 4A, a system that incorporates thelens assembly 10 may change the drive voltage V_(coil) across the coil18 in two component steps 30 and 32 having respective amplitudes A₁ andA₂, where the second component step 32 begins approximately a time T/2after the first component step 30, where T is the period at which eachof the component steps causes the lens assembly to oscillate, andwherein A₁+A₂=G=V₂−V₁.

Referring to FIGS. 1 and 4A-4B, the V_(coil) components 30 and 32 ofFIG. 4A set up respective oscillation components 34 and 36 in the lensassembly 10, where the components 34 and 3 substantially cancel oneanother. The components 34 and 36 have the same oscillation frequencyf_(d), but have different respective steady-state amplitudes D₁ and D₂such that x₂=++D₂. But because the V_(coil) component 32 is applied tothe coil 18 approximately a time T/2 (T=1/f_(d)) after the V_(coil)component 30 is applied to the coil, the oscillation component 36 isshifted by approximately 180° relative to the oscillation component 34.Therefore, the oscillations (i.e., the overshoot and undershootportions) of the component 36 substantially cancel the oscillations ofthe component 34 starting at approximately time T/2. For example, thepeaks of the oscillating component 34 are substantially aligned with,and thus substantially cancel, the valleys of the oscillating component36, and vice-versa.

Consequently, referring to FIG. 4C, starting at time T/2, the sum of theoscillation components 34 and 36 equals an approximately constantposition x₂=+D₁+D₂. That is, one may effectively increase the dampinglevel of an under-damped system without decreasing the system's responsetime (e.g., the time it takes for the lens 12 to travel from position x1to position x2 in FIG. 4C) by driving the system with a waveform similarto that of FIG. 4A

Referring to FIGS. 1 and 4A-4C, such a technique may reduce both theovershoot/undershoot amplitude and the settling time of the lensassembly 10. And this technique may accomplish such a reduction withoutmodifying the physical characteristics (e.g., the damping level ordamping coefficient) of the lens assembly 10. Therefore, this techniquemay reduce the time and cost of manufacturing a system such as a lensassembly 10, because the overshoot/undershoot amplitude, the settlingtime, or both the overshoot/undershoot amplitude and the settling time,of the system may be adjusted by programming/modifying the drivewaveform instead of physically modifying the system.

Still referring to FIGS. 1 and 4A-4C, an embodiment for calculating theamplitudes A₁ and A₂ of the V_(coil) components 30 and 32 is described.

The position x with respect to time t of a second-order system such asthe lens assembly 10 may be described according to the followingequation:

x(t)=P(1−e ^(−ζω) ^(d) ^(t)(A cos ω_(d) t+B sin ω_(d) t))  (1)

where P is the step in the position x applied to the system, ζ is thedamping coefficient of the system, ω₀ is the natural radial frequency ofthe system, and ω_(d) is the damped natural radial frequency of thesystem (ω_(d)=ω₀√{square root over (1−ζ²)})−ω_(d) is the actual radialfrequency of the decaying oscillations of an under-damped system.

Therefore, x(t) for each of the position components 34 and 36 is givenby the following equations:

$\begin{matrix}{{x_{34}(t)} = {D_{1}\left( {1 - {^{{- {ϛ\omega}_{0}}t}\left( {{A\; \cos \; \omega_{d}t} + {B\; \sin \; \omega_{d}t}} \right)}} \right)}} & (2) \\{{x_{36}(t)} = {D_{2}\left( {1 - {^{- {{ϛ\omega}_{0}{({t - \frac{T}{2}})}}}\left( {{A\; \cos \; {\omega_{d}\left( {t - \frac{T}{2}} \right)}} + {B\; \sin \; {\omega_{d}\left( {t - \frac{T}{2}} \right)}}} \right)}} \right)}} & (3)\end{matrix}$

For the oscillations of the components 34 and 36 to effectively cancelsuch that these components sum to a substantially constant positionD_(tot)=D₁+D₂ starting at time T/2, one may set the sum of equations (2)and (3) equal to D₁+D₂=D_(tot) starting at time T/2 as follows:

$\begin{matrix}{{{D_{1}\left( {1 - {^{{- {ϛ\omega}_{0}}t}\left( {{A\; \cos \; \omega_{d}t} + {B\; \sin \; \omega_{d}t}} \right)}} \right)} + {D_{2}\left( {1 - {^{- {{ϛ\omega}_{0}{({t - \frac{T}{2}})}}}\left( {{A\; \cos \; {\omega_{d}\left( {t - \frac{T}{2}} \right)}} + {B\; \sin \; {\omega_{d}\left( {t - \frac{T}{2}} \right)}}} \right)}} \right)}} = D_{tot}} & (4)\end{matrix}$

Because equation (4) holds at all values of t≧T/2, one may solve for D₁by setting t=T/2 and by setting D₂=D_(tot)−D₁ in equation (4).Therefore, D₁ and D₂ are given by the following equations:

$\begin{matrix}{D_{1} = \frac{D_{tot}}{1 + ^{{- {ϛ\omega}_{0}}\frac{T}{2}}}} & (5) \\{D_{2} = {D_{tot}\left( {1 - \frac{1}{1 + ^{{- {ϛ\omega}_{0}}\frac{T}{2}}}} \right)}} & (6)\end{matrix}$

And in an embodiment where G=V₂−V₁ (FIG. 4A) is a constant multiple ofD_(tot)—one may determine the relationship between G and D_(tot) bytesting the lens assembly 10 to develop a general relationship betweenthe position x of the lens 12 and the coil voltage V_(coil)—then A₁ andA₂ are given by the following equations:

$\begin{matrix}{A_{1} = \frac{G}{1 + ^{{- {ϛ\omega}_{0}}\frac{T}{2}}}} & (7) \\{A_{2} = {G\left( {1 - \frac{1}{1 + ^{{- {ϛ\omega}_{0}}\frac{T}{2}}}} \right)}} & (8)\end{matrix}$

Furthermore, for ζ<<1 (e.g., ζ=0.05), one may approximate A₁ and A₂ fromequations (7) and (8) as:

A ₁ =G(0.5+ζ)  (9)

A ₂ =G(0.5−ζ)  (10)

The values of A₁ and A₂ for an expected range of G may be stored in alook-up table (omitted from FIG. 1) of the system that incorporates thelens assembly 10.

Still referring to FIGS. 4A-4C, other embodiments of this technique arecontemplated. For example, Vcoil may have more than two components thatset up more than two position components in the lens assembly 10 suchthat the position components sum to substantially a constant value aftera particular time period has elapsed.

FIG. 5 is a diagram of an embodiment of a drive circuit 40 forgenerating the coil drive voltage V_(coil) according to an embodiment ofthe plot of FIG. 4A.

The drive circuit 40 includes an input node 42, first and secondprogrammable drive-signal generators 44 and 46 for respectivelygenerating the components 30 and 32 of V_(coil), a programmable delay 48for delaying the component 32, a combiner 50 for generating V_(coil)from the component 30 and the delayed component 32, and an output node52 coupled to the coil 18 of the lens assembly 10 of FIG. 1.

In operation, the system in which the lens assembly 10 is installedgenerates at the input node 42 an input signal representing or havingthe amplitude of the voltage V₂ needed to move the lens 12 from aposition x₁ to a position x₂, where the difference V₂−V₁ (the currentdrive voltage)=G.

The signal generator 44 generates a signal representing or having theamplitude V₁+A₁ (A₁ is the amplitude of the component 30), and thesignal generator 46 generates a signal representing or having theamplitude A₂ of the component 32. For example, the signal generators 44and 46 may obtain the amplitudes A₁ and A₂ from one or more look-uptables (not shown in FIG. 5) in response to the value G. The systemwhich incorporates the lens assembly 10 may provide the value G to thegenerators 44 and 46 (or to associated look-up tables), or thegenerators may calculate G from V₁ and V₂. Furthermore, the generator 44may generate the component 30 by subtracting approximately A₂ from theinput signal on the node 42.

The delay 48 generates a signal representing or having zero amplitudefor a programmed delay time, such as T/2, and thereafter generates asignal representing or having the amplitude A₂ of the component 32. Forexample, where the desired programmed delay time is T/2, then one mayprogram the delay 48 to have a duration that approximates T/2 and thatis given by the following equation:

$\begin{matrix}{{\Delta \; t} = {\frac{T}{2} = {\frac{\pi}{{\omega_{0}\sqrt{1 - ϛ^{2}}}\;} \approx \frac{\pi}{\omega_{0}}}}} & (11)\end{matrix}$

-   -   The delay 48 may obtain the value of Δt from a look-up table        (omitted from FIG. 5) in response to the value of T, where the        look-up table stores values of Δt for an anticipated range of T.        And Δt may have a resolution suitable for the application for        which the drive circuit 40 is being used.

The combiner generates on the output node 52 the coil drive signalV_(coil) having an amplitude equal to approximately V₁+A₁ from time t=0to time t˜T/2, and equal to approximately V₁+A₁+A₂=V₂ thereafter. Forexample, the combiner may be an adder.

Still referring to FIG. 5, alternate embodiments of the circuit 40 arecontemplated. For example, instead of generating the coil drive voltageV_(coil), the circuit 40 may generate the coil drive current I_(coil).Furthermore, the circuit 40 may be modified to drive second-ordersystems other than a lens assembly. Moreover, if V_(coil) on the outputnode 52 is in digital form, then the circuit 40 may include adigital-to-analog converter (DAC) to generate V_(coil) in analog form.In addition, the signal generated by the combiner 50 may representV_(coil), and one or more other circuits may generate V_(coil) and applyV_(coil) to the coil 18. Furthermore, any signal referred to as avoltage may be a current.

FIG. 5A is a diagram of an embodiment of the programmable signalgenerator 44 of FIG. 5. Because the signal generator 44 is programmable,it may be used with a wide variety of lens assemblies or othersecond-order systems having a wide range of response characteristics.

The signal generator 44 includes adders 54 and 56 and a multiplier 58.

In operation, the adder 54 subtracts G from V₂=V₁=G to generate a signalrepresenting or having the amplitude V₁. The adder 54 may receive G fromthe controller (omitted from FIG. 5A) for the system in which the signalgenerator 44 is installed, or from another suitable source.

The multiplier 58 multiplies G by

$\frac{1}{1 + ^{{- {ϛ\omega}_{0}}\frac{T}{2}}}$

to generate a signal representing or having the amplitude A₁ perequation (7). The multiplier 58 may be programmed with the value

$\frac{1}{1 + ^{{- {ϛ\omega}_{0}}\frac{T}{2}}},$

or may receive this value from the system controller (omitted from FIG.5A) or from a look-up table (omitted from FIG. 5A). Or, the multiplier58 may receive only the value of T or T/2 from the controller or alook-up table, and derive the multiplier

$\frac{1}{1 + ^{{- {ϛ\omega}_{0}}\frac{T}{2}}}$

from this value. Alternatively, the multiplier 58 may multiply G by(0.5+ζ) per equation (9), and may be programmed with the value ζ, or mayreceive this value from the system controller or a look-up table.

The adder 56 sums the signals from the adder 54 and the multiplier 58 togenerate on the output node 52 the drive-signal component 30, whichrepresents or has the amplitude V₁+A₁.

Still referring to FIG. 5A, alternate embodiments of the signalgenerator 44 are contemplated. For example, V₁ may be zero. Furthermore,the signal generator 46 of FIG. 5 may include only a multiplier thatgenerates A₂ from G according to equation (8) or equation (10).

FIG. 6 is a diagram of an embodiment of a drive circuit 60 forgenerating the coil drive voltage V_(coil) according to an embodiment ofthe plot of FIG. 4A.

The drive circuit 60 includes an input node 62, a counter 64 having anoutput node 66, a programmable drive-signal generator 68 for generatingthe component 30 (FIG. 4A) of V_(coil), a multiplexer 70, an optionalDAC 72, and an output node 74 coupled to the coil 18 of the lensassembly 10 of FIG. 1.

In operation, the system in which the lens assembly 10 is installedgenerates at the input node 42 an input signal representing or having anamplitude equal to the voltage V₂ needed to move the lens 12 from aposition x₁ to a position x₂.

In response to the input signal, the counter 64 begins counting. Thecounter 64 is programmed to output on the node 66 a selection signalhaving a first value starting from the counter's reception of the inputsignal until a duration approximately equal to T/2 has elapsed, andhaving a second value thereafter. Count values Δt (approximately equalto T/2) for the counter 64 may be calculated according to equation (11)and stored in a look-up table (omitted from FIG. 6) for an expectedrange of T.

The signal generator 68 generates from the input signal a componentdrive signal representing or having the amplitude V₁+A₁ of the component30 of FIG. 4A. For example, the generator 68 may subtract from the inputsignal a programmed value approximately equal to A₂. This value may becalculated from G and equation (8) or (10), or obtained from a look-uptable (omitted from FIG. 6). An embodiment of the signal generator 68may be similar to the signal generator 44 of FIGS. 5 and 5A.

The multiplexer 70 outputs the component 30 from the generator 68 inresponse to the counter output signal having the first value (i.e.,before the counter value reaches approximately T/2), and then outputsthe input signal in response to the counter output signal having thesecond value (i.e., after the counter value reaches approximately T/2).

The DAC 72 converts the multiplexer output into the analog version ofthe drive voltage V_(coil) on the output node 74.

Still referring to FIG. 6, alternate embodiments of the circuit 60 arecontemplated. For example, one or more of the alternate embodimentsdescribed above in conjunction with the circuit 40 of FIG. 5 may beapplied to the circuit 60.

FIG. 7 is a diagram of an embodiment of a system, such as a camerasystem 80, that may incorporate the lens assembly 10 of FIG. 1 and anembodiment of the lens drive circuit 40 of FIG. 5 or of the lens drivecircuit 60 of FIG. 6. But for example purposes, the system 80 isdescribed as including an embodiment of the lens drive circuit 60 ofFIG. 6.

In addition to the lens assembly 10 and the lens drive circuit 60, thecamera system 80 includes a controller 82 for generating the drivevoltage (e.g., V₂) on the drive-circuit input node 62 (FIG. 6) and asignal representing the change G in the drive voltage, and for otherwisecontrolling the operation of the camera system. The controller 82 maygenerate the drive voltage and the signal representing G in response toone or more circuits, such as an auto- or manual-focus circuit (omittedfrom FIG. 7), or in response to an operator input (e.g., pressing afocus button).

The camera system 80 may also include a pixel array 84 for capturing animage, where the lens assembly 10 causes the lens 12 to focus the imageonto the pixel array.

The circuit 60, controller 82, and pixel array 84, as well as any othercircuits of the camera 80, may be disposed on a same or on differentintegrated circuits (ICs) and on a same or on different IC dies.

Although described as a camera system including a lens assembly, thesystem 80 may be any other type of system that incorporates asecond-order subsystem other than a lens assembly, and the drive circuit60 may be modified to drive such another second order subsystem.

From the foregoing it will be appreciated that, although specificembodiments have been described herein for purposes of illustration,various modifications may be made without deviating from the spirit andscope of the disclosure. Furthermore, where an alternative is disclosedfor a particular embodiment, this alternative may also apply to otherembodiments even if not specifically stated.

1. A circuit, comprising: a first generator operable to generate a firstdrive signal; and a second signal generator operable to receive thefirst drive signal and a second drive signal, and to generate from thefirst and second drive signals a system drive signal having a firstamplitude for a first duration and having a second amplitude after thefirst duration, the system drive signal operable to cause anunder-damped system to operate in a substantially damped manner.
 2. Thecircuit of claim 1, further comprising a third signal generator operableto generate the second drive signal.
 3. The circuit of claim 1 wherein:the first generator is operable to generate the first drive signalhaving approximately the first amplitude; and the second generator isoperable to receive the second drive signal having approximately thesecond amplitude.
 4. The circuit of claim 1, further comprising: whereinthe first generator is operable to generate the first drive signalhaving approximately the first amplitude; and a third generator operableto generate the second drive signal having approximately a thirdamplitude that is approximately equal to a difference between the firstand second amplitudes.
 5. The circuit of claim 1, further comprising:wherein the first generator is operable to generate the first drivesignal having approximately the first amplitude; and a third generatoroperable to receive a third drive signal and to generate from the thirddrive signal the second drive signal having approximately a thirdamplitude that is approximately equal to a difference between the firstand second amplitudes.
 6. The circuit of claim 1, further comprising:wherein the first generator is operable to generate the first drivesignal having approximately the first amplitude; a third generatoroperable to generate the second drive signal having approximately athird amplitude that is approximately equal to a difference between thefirst and second amplitudes; and wherein the second generator isoperable to combine the first and second drive signals after the firstduration.
 7. The circuit of claim 1 wherein the second signal generatoris operable to generate the system drive signal by delaying the seconddrive signal relative to the first drive signal.
 8. The circuit of claim1 wherein the second signal generator is operable to generate the systemdrive signal by delaying the second drive signal relative to the firstdrive signal by approximately half of a period of a response frequencyof the system.
 9. The circuit of claim 1, further comprising a thirdgenerator operable to generate the second drive signal delayed relativeto the first drive signal.
 10. The circuit of claim 1, furthercomprising a third generator operable to generate the second drivesignal delayed relative to the first drive signal by approximately halfof a period of a response frequency of the system.
 11. The circuit ofclaim 1 wherein the first generator is operable to receive the seconddrive signal and to generate the first drive signal from the seconddrive signal.
 12. A system, comprising: an under-damped subsystem; and acircuit operable to drive the subsystem, the circuit including: a firstgenerator operable to generate a first drive signal; and a second signalgenerator operable to receive the first drive signal and a second drivesignal, and to generate from the first and second drive signals a systemdrive signal having a first amplitude for a first duration and having asecond amplitude after the first duration, the system drive signaloperable to cause the under-damped subsystem to operate in asubstantially damped manner.
 13. The system of claim 12 wherein theunder-damped subsystem comprises an under-damped second-order subsystem.14. The system of claim 12 wherein the under-damped subsystem comprisesan electric motor.
 15. The system of claim 12 wherein the under-dampedsubsystem comprises a spring-loaded voice-coil motor.
 16. The system ofclaim 12 wherein the under-damped subsystem comprises a lens assembly.17. The system of claim 12, further comprising a controller operable togenerate the second drive signal.
 18. The system of claim 12, furthercomprising: a controller operable to generate the second drive signal;and wherein the first signal generator is operable to generate the firstdrive signal from the second drive signal.
 19. The system of claim 12,further comprising: a controller operable to generate a third drivesignal; a third signal generator operable to generate the second drivesignal from the third drive signal; and wherein the first signalgenerator is operable to generate the first drive signal from the thirddrive signal.
 20. A method, comprising: driving an under-damped systemwith a drive signal having a first magnitude for a first period; andchanging the first magnitude of the drive signal to a second magnitudein response to an end of the first period.
 21. The method of claim 20wherein the second magnitude is greater than the first magnitude. 22.The method of claim 20 wherein the first period is approximately equalto half a period of a damped resonant frequency of the system.
 23. Themethod of claim 20, further comprising: generating the drive signal froma first signal having the first magnitude during the first period; andgenerating the drive signal from a second signal having the secondmagnitude in response to the end of the first period.
 24. The method ofclaim 20, further comprising: generating the drive signal from a firstsignal having the first magnitude during the first period; generating asecond signal having a magnitude approximately equal to a differencebetween the first and second magnitudes; and generating the drive signalfrom a combination of the first and second signals in response to theend of the first period.
 25. The method of claim 20, further comprising:generating the drive signal from a first signal having the firstmagnitude during the first period; generating a second signal having amagnitude approximately equal to a difference between the first andsecond magnitudes; delaying the second signal by approximately the firstperiod; and generating the drive signal from a combination of the firstsignal and the delayed second signal.
 26. A method, comprising: causingan under-damped system to oscillate at a damped frequency having a firstphase; and causing the system to oscillate at substantially the dampedfrequency having a second phase such that the oscillation at the firstphase substantially cancels the oscillation at the second phase.
 27. Themethod of claim 26, further comprising causing the system to oscillateat the second phase a time after causing the system to oscillate at thefirst phase.
 28. The method of claim 26, further comprising causing thesystem to oscillate at the second phase approximately one half of theoscillation period after causing the system to oscillate at the firstphase.
 29. The method of claim 26 wherein the difference between thefirst and second phases is approximately 180 degrees.
 30. The method ofclaim 26 wherein the oscillations at the first and second phasescomprise respective decaying oscillations.
 31. The method of claim 26wherein the oscillations at the first and second phases compriserespective exponentially decaying oscillations.
 32. The method of claim26, further comprising: scaling the oscillations at the first phase by afirst factor; scaling the oscillations at the second phase by a secondfactor; and wherein a position of the system approaches a sum of thefirst and second factors over time.
 33. The method of claim 26, furthercomprising: causing the oscillations at the first phase by applying anapproximately step input of a first amplitude to the system at a firsttime; and causing the oscillations at the second phase by applying anapproximately step input of a second amplitude to the system at a secondtime.
 34. The method of claim 26 wherein: the second time is subsequentto the first time; and the first amplitude is greater than the secondamplitude.